-- Copyright (c) 2011, Colin Hill
--
-- Loosely based on implementation of libnoise by Jason Bevins Copyright (C) 2003, 2004
-- http://libnoise.sourceforge.net

-- | Contains 'Noise' class as well as a general coherent noise generating function which
-- the specific noise implementations are based on.
module Numeric.Noise (
    Point,
    Seed,
    Noise(noiseValue),
    pmap,
    clamp,
    coherentNoise
) where

import Data.Bits
import Data.Vector.Unboxed (Vector, fromList, (!))

-- | A point in 3-space.
type Point = (Double, Double, Double)

-- | A seed for a random function.
type Seed = Int

-- | Class of noise functions.
class Noise a where
    -- | Maps 3-space points to a noise value between -1 and 1 for the given noise function.
    noiseValue :: a -> Point -> Double

-- | Map a function on a 'Point'.
pmap :: (Double -> Double) -> Point -> Point
pmap f (x, y, z) = (f x, f y, f z)

-- | Returns a clamped value between a min and max value.
clamp :: Ord a => a -> a -> a -> a
clamp v m m' = max m (min m' v)

-- | Returns a coherent noise value between -1 and 1 given a seed and a point in 3-space.
coherentNoise :: Seed -> Point -> Double
coherentNoise seed (x, y, z) = clamp noise (-1) 1
    where (ox, oy, oz) = (clampToIntRange x, clampToIntRange y, clampToIntRange z)
          x0           = if ox > 0.0 then floor ox else floor ox - 1
          x1           = x0 + 1
          y0           = if oy > 0.0 then floor oy else floor oy - 1
          y1           = y0 + 1
          z0           = if oz > 0.0 then floor oz else floor oz - 1
          z1           = z0 + 1
          sx           = scurve (ox - fromIntegral x0)
          sy           = scurve (oy - fromIntegral y0)
          sz           = scurve (oz - fromIntegral z0)
          n0           = gradientNoise seed ox oy oz x0 y0 z0
          n1           = gradientNoise seed ox oy oz x1 y0 z0
          n2           = gradientNoise seed ox oy oz x0 y1 z0
          n3           = gradientNoise seed ox oy oz x1 y1 z0
          n4           = gradientNoise seed ox oy oz x0 y0 z1
          n5           = gradientNoise seed ox oy oz x1 y0 z1
          n6           = gradientNoise seed ox oy oz x0 y1 z1
          n7           = gradientNoise seed ox oy oz x1 y1 z1
          ix0          = lerp sx n0 n1
          ix1          = lerp sx n2 n3
          ix2          = lerp sx n4 n5
          ix3          = lerp sx n6 n7
          iy0          = lerp sy ix0 ix1
          iy1          = lerp sy ix2 ix3
          noise        = lerp sz iy0 iy1

-- | Returns a gradient noise value given a seed, a point in 3-space, and a nearby integer
-- point in 3-space.
gradientNoise :: Seed -> Double -> Double -> Double -> Int -> Int -> Int -> Double
gradientNoise seed fx fy fz ix iy iz = 2.12 * (gx * ox + gy * oy + gz * oz)
    where (gx, gy, gz) = (vectorTable ! shiftL i 2,
                          vectorTable ! (shiftL i 2 + 1),
                          vectorTable ! (shiftL i 2 + 2))
          (ox, oy, oz) = (fx - fromIntegral ix,
                          fy - fromIntegral iy,
                          fz - fromIntegral iz)
          i            = (i' `xor` shiftR i' 8) .&. 0xff
          i'           = (1619 * ix + 31337 * iy + 6971 * iz + 1013 * seed) .&. 0xffffffff

-- | Returns the linearly interpolated value between two values given a delta.
lerp :: Double -> Double -> Double -> Double
lerp t a b = (1.0 - t) * a + t * b

-- | Maps a value onto a quintic s-curve.
scurve :: Double -> Double
scurve a = (6.0 * a5) - (15.0 * a4) + (10.0 * a3)
    where a3 = a * a * a
          a4 = a3 * a
          a5 = a4 * a

-- | Clamps a 'Double' to the range of an 'Int'.
clampToIntRange :: Double -> Double
clampToIntRange n | n >= maxInt    = 2.0 * fmod n maxInt - maxInt
                  | n <= (-maxInt) = 2.0 * fmod n maxInt + maxInt
                  | otherwise            = n
    where maxInt = 1073741824.0 -- Max 32 bit signed Int.  Should not be hardcoded.

-- | Floating point modulus function.
fmod :: Double -> Double -> Double
fmod x y = x - fromIntegral (floor (x / y) :: Int) * y

-- | Table of random normalized vectors.
vectorTable :: Vector Double
vectorTable = fromList [
    -0.763874, -0.596439, -0.246489, 0.0,
    0.396055, 0.904518, -0.158073, 0.0,
    -0.499004, -0.8665, -0.0131631, 0.0,
    0.468724, -0.824756, 0.316346, 0.0,
    0.829598, 0.43195, 0.353816, 0.0,
    -0.454473, 0.629497, -0.630228, 0.0,
    -0.162349, -0.869962, -0.465628, 0.0,
    0.932805, 0.253451, 0.256198, 0.0,
    -0.345419, 0.927299, -0.144227, 0.0,
    -0.715026, -0.293698, -0.634413, 0.0,
    -0.245997, 0.717467, -0.651711, 0.0,
    -0.967409, -0.250435, -0.037451, 0.0,
    0.901729, 0.397108, -0.170852, 0.0,
    0.892657, -0.0720622, -0.444938, 0.0,
    0.0260084, -0.0361701, 0.999007, 0.0,
    0.949107, -0.19486, 0.247439, 0.0,
    0.471803, -0.807064, -0.355036, 0.0,
    0.879737, 0.141845, 0.453809, 0.0,
    0.570747, 0.696415, 0.435033, 0.0,
    -0.141751, -0.988233, -0.0574584, 0.0,
    -0.58219, -0.0303005, 0.812488, 0.0,
    -0.60922, 0.239482, -0.755975, 0.0,
    0.299394, -0.197066, -0.933557, 0.0,
    -0.851615, -0.220702, -0.47544, 0.0,
    0.848886, 0.341829, -0.403169, 0.0,
    -0.156129, -0.687241, 0.709453, 0.0,
    -0.665651, 0.626724, 0.405124, 0.0,
    0.595914, -0.674582, 0.43569, 0.0,
    0.171025, -0.509292, 0.843428, 0.0,
    0.78605, 0.536414, -0.307222, 0.0,
    0.18905, -0.791613, 0.581042, 0.0,
    -0.294916, 0.844994, 0.446105, 0.0,
    0.342031, -0.58736, -0.7335, 0.0,
    0.57155, 0.7869, 0.232635, 0.0,
    0.885026, -0.408223, 0.223791, 0.0,
    -0.789518, 0.571645, 0.223347, 0.0,
    0.774571, 0.31566, 0.548087, 0.0,
    -0.79695, -0.0433603, -0.602487, 0.0,
    -0.142425, -0.473249, -0.869339, 0.0,
    -0.0698838, 0.170442, 0.982886, 0.0,
    0.687815, -0.484748, 0.540306, 0.0,
    0.543703, -0.534446, -0.647112, 0.0,
    0.97186, 0.184391, -0.146588, 0.0,
    0.707084, 0.485713, -0.513921, 0.0,
    0.942302, 0.331945, 0.043348, 0.0,
    0.499084, 0.599922, 0.625307, 0.0,
    -0.289203, 0.211107, 0.9337, 0.0,
    0.412433, -0.71667, -0.56239, 0.0,
    0.87721, -0.082816, 0.47291, 0.0,
    -0.420685, -0.214278, 0.881538, 0.0,
    0.752558, -0.0391579, 0.657361, 0.0,
    0.0765725, -0.996789, 0.0234082, 0.0,
    -0.544312, -0.309435, -0.779727, 0.0,
    -0.455358, -0.415572, 0.787368, 0.0,
    -0.874586, 0.483746, 0.0330131, 0.0,
    0.245172, -0.0838623, 0.965846, 0.0,
    0.382293, -0.432813, 0.81641, 0.0,
    -0.287735, -0.905514, 0.311853, 0.0,
    -0.667704, 0.704955, -0.239186, 0.0,
    0.717885, -0.464002, -0.518983, 0.0,
    0.976342, -0.214895, 0.0240053, 0.0,
    -0.0733096, -0.921136, 0.382276, 0.0,
    -0.986284, 0.151224, -0.0661379, 0.0,
    -0.899319, -0.429671, 0.0812908, 0.0,
    0.652102, -0.724625, 0.222893, 0.0,
    0.203761, 0.458023, -0.865272, 0.0,
    -0.030396, 0.698724, -0.714745, 0.0,
    -0.460232, 0.839138, 0.289887, 0.0,
    -0.0898602, 0.837894, 0.538386, 0.0,
    -0.731595, 0.0793784, 0.677102, 0.0,
    -0.447236, -0.788397, 0.422386, 0.0,
    0.186481, 0.645855, -0.740335, 0.0,
    -0.259006, 0.935463, 0.240467, 0.0,
    0.445839, 0.819655, -0.359712, 0.0,
    0.349962, 0.755022, -0.554499, 0.0,
    -0.997078, -0.0359577, 0.0673977, 0.0,
    -0.431163, -0.147516, -0.890133, 0.0,
    0.299648, -0.63914, 0.708316, 0.0,
    0.397043, 0.566526, -0.722084, 0.0,
    -0.502489, 0.438308, -0.745246, 0.0,
    0.0687235, 0.354097, 0.93268, 0.0,
    -0.0476651, -0.462597, 0.885286, 0.0,
    -0.221934, 0.900739, -0.373383, 0.0,
    -0.956107, -0.225676, 0.186893, 0.0,
    -0.187627, 0.391487, -0.900852, 0.0,
    -0.224209, -0.315405, 0.92209, 0.0,
    -0.730807, -0.537068, 0.421283, 0.0,
    -0.0353135, -0.816748, 0.575913, 0.0,
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    -0.283847, 0.533842, 0.796519, 0.0,
    -0.482737, -0.850448, 0.209052, 0.0,
    -0.649175, 0.477748, 0.591886, 0.0,
    0.885373, -0.405387, -0.227543, 0.0,
    -0.147261, 0.181623, -0.972279, 0.0,
    0.0959236, -0.115847, -0.988624, 0.0,
    -0.89724, -0.191348, 0.397928, 0.0,
    0.903553, -0.428461, -0.00350461, 0.0,
    0.849072, -0.295807, -0.437693, 0.0,
    0.65551, 0.741754, -0.141804, 0.0,
    0.61598, -0.178669, 0.767232, 0.0,
    0.0112967, 0.932256, -0.361623, 0.0,
    -0.793031, 0.258012, 0.551845, 0.0,
    0.421933, 0.454311, 0.784585, 0.0,
    -0.319993, 0.0401618, -0.946568, 0.0,
    -0.81571, 0.551307, -0.175151, 0.0,
    -0.377644, 0.00322313, 0.925945, 0.0,
    0.129759, -0.666581, -0.734052, 0.0,
    0.601901, -0.654237, -0.457919, 0.0,
    -0.927463, -0.0343576, -0.372334, 0.0,
    -0.438663, -0.868301, -0.231578, 0.0,
    -0.648845, -0.749138, -0.133387, 0.0,
    0.507393, -0.588294, 0.629653, 0.0,
    0.726958, 0.623665, 0.287358, 0.0,
    0.411159, 0.367614, -0.834151, 0.0,
    0.806333, 0.585117, -0.0864016, 0.0,
    0.263935, -0.880876, 0.392932, 0.0,
    0.421546, -0.201336, 0.884174, 0.0,
    -0.683198, -0.569557, -0.456996, 0.0,
    -0.117116, -0.0406654, -0.992285, 0.0,
    -0.643679, -0.109196, -0.757465, 0.0,
    -0.561559, -0.62989, 0.536554, 0.0,
    0.0628422, 0.104677, -0.992519, 0.0,
    0.480759, -0.2867, -0.828658, 0.0,
    -0.228559, -0.228965, -0.946222, 0.0,
    -0.10194, -0.65706, -0.746914, 0.0,
    0.0689193, -0.678236, 0.731605, 0.0,
    0.401019, -0.754026, 0.52022, 0.0,
    -0.742141, 0.547083, -0.387203, 0.0,
    -0.00210603, -0.796417, -0.604745, 0.0,
    0.296725, -0.409909, -0.862513, 0.0,
    -0.260932, -0.798201, 0.542945, 0.0,
    -0.641628, 0.742379, 0.192838, 0.0,
    -0.186009, -0.101514, 0.97729, 0.0,
    0.106711, -0.962067, 0.251079, 0.0,
    -0.743499, 0.30988, -0.592607, 0.0,
    -0.795853, -0.605066, -0.0226607, 0.0,
    -0.828661, -0.419471, -0.370628, 0.0,
    0.0847218, -0.489815, -0.8677, 0.0,
    -0.381405, 0.788019, -0.483276, 0.0,
    0.282042, -0.953394, 0.107205, 0.0,
    0.530774, 0.847413, 0.0130696, 0.0,
    0.0515397, 0.922524, 0.382484, 0.0,
    -0.631467, -0.709046, 0.313852, 0.0,
    0.688248, 0.517273, 0.508668, 0.0,
    0.646689, -0.333782, -0.685845, 0.0,
    -0.932528, -0.247532, -0.262906, 0.0,
    0.630609, 0.68757, -0.359973, 0.0,
    0.577805, -0.394189, 0.714673, 0.0,
    -0.887833, -0.437301, -0.14325, 0.0,
    0.690982, 0.174003, 0.701617, 0.0,
    -0.866701, 0.0118182, 0.498689, 0.0,
    -0.482876, 0.727143, 0.487949, 0.0,
    -0.577567, 0.682593, -0.447752, 0.0,
    0.373768, 0.0982991, 0.922299, 0.0,
    0.170744, 0.964243, -0.202687, 0.0,
    0.993654, -0.035791, -0.106632, 0.0,
    0.587065, 0.4143, -0.695493, 0.0,
    -0.396509, 0.26509, -0.878924, 0.0,
    -0.0866853, 0.83553, -0.542563, 0.0,
    0.923193, 0.133398, -0.360443, 0.0,
    0.00379108, -0.258618, 0.965972, 0.0,
    0.239144, 0.245154, -0.939526, 0.0,
    0.758731, -0.555871, 0.33961, 0.0,
    0.295355, 0.309513, 0.903862, 0.0,
    0.0531222, -0.91003, -0.411124, 0.0,
    0.270452, 0.0229439, -0.96246, 0.0,
    0.563634, 0.0324352, 0.825387, 0.0,
    0.156326, 0.147392, 0.976646, 0.0,
    -0.0410141, 0.981824, 0.185309, 0.0,
    -0.385562, -0.576343, -0.720535, 0.0,
    0.388281, 0.904441, 0.176702, 0.0,
    0.945561, -0.192859, -0.262146, 0.0,
    0.844504, 0.520193, 0.127325, 0.0,
    0.0330893, 0.999121, -0.0257505, 0.0,
    -0.592616, -0.482475, -0.644999, 0.0,
    0.539471, 0.631024, -0.557476, 0.0,
    0.655851, -0.027319, -0.754396, 0.0,
    0.274465, 0.887659, 0.369772, 0.0,
    -0.123419, 0.975177, -0.183842, 0.0,
    -0.223429, 0.708045, 0.66989, 0.0,
    -0.908654, 0.196302, 0.368528, 0.0,
    -0.95759, -0.00863708, 0.288005, 0.0,
    0.960535, 0.030592, 0.276472, 0.0,
    -0.413146, 0.907537, 0.0754161, 0.0,
    -0.847992, 0.350849, -0.397259, 0.0,
    0.614736, 0.395841, 0.68221, 0.0,
    -0.503504, -0.666128, -0.550234, 0.0,
    -0.268833, -0.738524, -0.618314, 0.0,
    0.792737, -0.60001, -0.107502, 0.0,
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    -0.732341, 0.680909, -0.0063274, 0.0,
    -0.760674, -0.141009, 0.633634, 0.0,
    0.222823, -0.304012, 0.926243, 0.0,
    0.209178, 0.505671, 0.836984, 0.0,
    0.757914, -0.56629, -0.323857, 0.0,
    -0.782926, -0.339196, 0.52151, 0.0,
    -0.462952, 0.585565, 0.665424, 0.0,
    0.61879, 0.194119, -0.761194, 0.0,
    0.741388, -0.276743, 0.611357, 0.0,
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    0.437895, 0.152598, -0.885981, 0.0,
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    0.212189, -0.815162, -0.538969, 0.0,
    -0.859262, 0.143405, -0.491024, 0.0,
    0.991353, 0.112814, 0.0670273, 0.0,
    0.0337884, -0.979891, -0.196654, 0.0]